Part A (55%)
Symbolize the following sentences using the scheme of abbreviations given:
A: Aaron is in the office.
B: Bryan is in the office.
J: Jerry goes home early.
S: It’s sunny.
T: It’s Tuesday.
W: It’s warm.
1. It’s neither sunny nor warm.
2. Aaron is in the office or Bryan isn’t.
3. Bryan is in the office only if it’s Tuesday.
4. If Aaron is in the office, then it’s Tuesday.
5. It’s Tuesday but Bryan is not in the office.
6. Aaron is in the office provided that Bryan is.
7. Jerry will go home early if it’s sunny or warm.
8. It’s Tuesday, and although it’s sunny, it’s not warm.
9. Jerry will go home early unless Aaron is in the office or it’s not sunny.
10. Bryan is in the office if and only if Jerry went home early and it isn’t warm.
11. If Aaron or Bryan is in the office, then if it’s sunny and warm, it’s not Tuesday.
Part B (30%)
Construct truth tables to answer the following questions. For each question, be sure to clearly state your answer (in addition to constructing the truth table) and use the correct procedure for constructing truth tables.
1. Is the sentence form below a tautology, a contradiction, or a contingency?
(~p & q) -> (p <-> ~q)
2. Is the following set of sentence forms consistent?
p -> q, ~q, ~p -> p
3. Are these two sentence forms equivalent?
p -> (q -> p), ~p v q
Part C (15%)
Use a shortened truth table to construct a counterexample to the following argument form.
~p <-> ~r
~q <-> ~r
/.: (p v q) -> ~r
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